Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Steady-state distribution

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_997

Let pij(t) be the probability that a stochastic process takes on value j at “time” t (discrete or continuous), given that it began at time 0 from state i. If pij(t) approaches a limit pj independent of i at t →∞ for all j, the set pv = {pj} is called the limiting or steady-state distribution of the process. For Markov chains in discrete time, the existence of a limiting distribution implies that there is a stationary distribution found from π = πPv and that π = p.v For continuous-time chains, the steady-state distribution is the probability vector satisfying the global balance equations πQv = 0.  Limiting distribution;  Markov chains;  Markov processes; Stationary distribution; Statistical equilibrium.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA